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Fully describe the plane defined by the equation y - z = 0. Be clear and...

Fully describe the plane defined by the equation y - z = 0. Be clear and organized with generalizations.

Math   Calculus   
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Answer #1

First think just of the YZ plane. Standing on it, y = z is a straight line passing through origin, equally inclined to both Y and Z axes.

When we extend this line to space, y = z becomes a plane which is an extension of the direction defined by the line, i.e. the plane is still equally inclined to both the Y and Z axes, just like the line was.

The parameters of interest that can be described about the plane are

Geogebra gives following sketch of the plane

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